This paper presents a computational scheme for compressible magnetohydrodynamics (MHD). The scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and solution-adaptive refinement and coarsening. In addition, a method for increasing the accuracy of the scheme by subtracting off an embedded steady magnetic field is presented. Each of the pieces of the scheme is described, and the scheme is validated and its accuracy assessed by comparison with exact solutions. Results are presented for two three-dimensional calculations representative of the interaction of the solar wind with a magenetized planet. © 1999 Academic Press.
Powell, K. G., Roe, P. L., Linde, T. J., Gombosi, T. I., & De Zeeuw, D. L. (1999). A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics. Journal of Computational Physics, 154(2), 284–309. https://doi.org/10.1006/jcph.1999.6299